Abstract
In this paper, we propose two SUR type estimators based on combining the SUR ridge regression and the restricted least squares methods. In the sequel these estimators are designated as the restricted ridge Liu estimator and the restricted ridge HK estimator (see Liu in Commun Statist Thoery Methods 22(2):393–402, 1993; Sarkar in Commun Statist A 21:1987–2000, 1992). The study has been made using Monte Carlo techniques, (1,000 replications), under certain conditions where a number of factors that may effect their performance have been varied. The performance of the proposed and some of the existing estimators are evaluated by means of the TMSE and the PR criteria. Our results indicate that the proposed SUR restricted ridge estimators based on K SUR, K Sratio, K Mratio and \({\ddot{K}}\) produced smaller TMSE and/or PR values than the remaining estimators. In contrast with other ridge estimators, components of \({\ddot{K}}\) are defined in terms of the eigenvalues of \({X^{{\ast^{\prime}}} X^{\rm \ast}}\) and all lie in the open interval (0, 1).
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Alkhamisi MA, Shukur G (2007) A Monte Carlo study of recent ridge parameters. Commun Stat Simulat Comput 3(36): 535–547
Alkhamisi MA, Shukur G (2008) Developing ridge parameters for SUR model. Commun Stat Thoery Methods 37(4): 544–564
Akdeniz F, Kaciranlar S (2001) More on the new biased estimator in linear regression. Indian J Stat 63(3): 321–325
Brown PJ (1977) Centering and scaling in ridge regression. Tecnometrics 19: 35–36
Brown PJ, Payne C (1975) Election night forecasting (with discussion). J R Stat Soc Ser A 138: 463–498
Chib S, Greenberg E (1995) Hierarchical analysis of SUR model with extensions to correlated serial errors and time varying parameter models. J Econ 68: 339–360
Edgerton DL, Assarsson B, Hummelmose A, Laurila IP, Ricertsen K, Vlae PH (1996) The econometrics of demand systems. Kluwer, Dordrecht
Gross J (2003) Restricted ridge estimation. Stat Prob Lett 65: 57–64
Hoerl AE, Kennard RW (1970a) Ridge regression: biased estimation for non-orthogonal problems. Tech 12: 55–67
Hoerl AE, Kennard RW (1970b) Ridge regression: application to non- orthogonal problems. Tech 12: 69–82
Johnson N, Kotz S, Balakrishnan N (2000) Continuous multivariat distributions, 2nd edn, vol 1. Wiley, New York
Kibria BMG (2003) Performance of some new ridge regression estimators. Commun Stat B 32(2): 419–435
Koop G (2003) Bayesian econometrics. Wiley, New York
Liu K (1993) A new biased estimate in linear regression. Commun Stat Thoery Methods 22(2): 393–402
MacDonald GC, Galarneau DI (1975) A Monte-Carlo evaluation of some ridge-type estimators. J Am Stat Assoc 70: 407–416
Rao CR (1973) Linear statistical inference and its applications. Wiley, New York
Rao CR (1975) Simultaneous estimation of parameters in different linear models and applications to biometric problems. Biometrics 3(2): 545–554
Sarkar N (1992) A new estimator combining the ridge regression and the restricted least squares method of estimation. Commun Stat A 21: 1987–2000
Sarkar N (1998) Erratum: a new estimator combining the ridge regression and the restricted least squares method of estimation. Commun Stat A 27: 1019–1020
Shukur G (2002) Dynamic specification and misspecification in systems of demand equations; a testing strategy for model selection. Appl Econ 34: 709–725
Srivastava V, Giles D (1987) Seemingly unrelated regression equations models. Marcel Dekker, New York
Vinod HD (1978) A survey of ridge regression and related techniques for improvements over ordinary least squares. Rev Econ Stat 60: 121–131
Zellner A (1962) An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J Am Stat Assoc 57: 348–68
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Alkhamisi, M.A. Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies. Stat Papers 51, 651–672 (2010). https://doi.org/10.1007/s00362-008-0151-2
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DOI: https://doi.org/10.1007/s00362-008-0151-2
Keywords
- Multicollinearity
- Restricted generalized least squares estimator
- SUR restricted ridge estimator
- Liu estimator
- Biased estimator
- Monte Carlo simulation